Efficient simulation of discrete stochastic reaction systems with a splitting method

Date

2010-01-01

Author

Jahnke, Tobias
Altıntan, Derya

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Stochastic reaction systems with discrete particle numbers are usually described by a continuous-time Markov process. Realizations of this process can be generated with the stochastic simulation algorithm, but simulating highly reactive systems is computationally costly because the computational work scales with the number of reaction events. We present a new approach which avoids this drawback and increases the efficiency considerably at the cost of a small approximation error. The approach is based on the fact that the time-dependent probability distribution associated to the Markov process is explicitly known for monomolecular, autocatalytic and certain catalytic reaction channels. More complicated reaction systems can often be decomposed into several parts some of which can be treated analytically. These subsystems are propagated in an alternating fashion similar to a splitting method for ordinary differential equations. We illustrate this approach by numerical examples and prove an error bound for the splitting error. © 2010 Springer Science + Business Media B.V.

Subject Keywords

Analytic solution formulas, Chemical master equation, Discrete stochastic reaction systems, Error bounds, Splitting methods, Stochastic simulation algorithm

URI

https://hdl.handle.net/11511/107685

Collections

Graduate School of Applied Mathematics, Article